The United States Air Force Academy, in response to the “Chips Ahoy! 1,000 Chips Challenge”, calculated that there were a total of 52,986 chocolate chips in 42 18-ounce bags of Chips Ahoy! cookies. The sample mean is 1261.6 and the sample standard deviation is 117.6.
Each 18-ounce bag of cookies contains 48 individual cookies. If a single cookie is picked at random, which of the following numbers of chocolate chips is it most likely to have:
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i agree the sol. you cannot round off 26.28 cookies to 26, that 0.28 part is obtained from the 27th cookie, so therefore there are 27 cookies,
i did the same
26.283 is near to 26 rather than 27 . then how 27 ??
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Sometimes you have to look in the options too.. :P
1261.6 divided by 42 will get you around 30 (the mean number of chips in a random cookie)
117.6 divided by 42 will get you 2.8, round off to 3 (Standard deviation)
so the answer should be...
30 +/- 3...... either 27 or 33
you have to divide by 48. You will get 26.2 +/- 2.5, which is closest to 27.
Total chip spread over the cookies equally in every bag : 52,986/42/48 = 26.2 (say 27).
But there were 48 cookies per bag so the range of possible amounts of chips were 29-23. I thus chose 25 because it was closer to 26 which would be the mean of that range of numbers which answer wasn't a possible answer, but 27 is equally close to 26 which would be the answer if it were a possible choice. So it could be 25 or 27.
The mean number of chocolate chips in the sample is 1261.6 per bag. Since there are 48 cookies per bag, the mean number of chocolate chips per cookie is: 4 8 1 2 6 1 . 6 = 2 6 . 2 8 3
The possible choice closest to this answer is 2 7 .
26.283 is near to 26 not 27 ? ??
There are multiple distractions in this question. There is a sample size, and standard deviation. Don't go calculating standard errors (SE) here. Not necessary yet. The question is simply: If a cookie is chosen, how many chocolate chips will it have on an average?
The question actually boils down to 3 steps:
a) The number of cookies in the bag -- 48
b) The number of chocolate chips in a bag of Chips ahoy -- 1261.6
Hence, <b> average number of chips per cookie = 1261.6/48 = 26.28 </b>
c) You don't see this exact answer (how can you have .28 of a chip? :)) but since the question asks "most likely", you know you need to find the closest number to 26.28, i.e. 27
Well, this is a correct solution
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There are 1261.6 chips/bag Each bag has 42 pieces of cookies so, there are about 1261.6/42 = 26.28 => 27 chips/cookies